@CarmenBurrito, you've had some great advice above. I also have a performing DC, who did a lot of professional theatre when he was younger and is now learning to negotiate the post-licence acting world (until age 16, children need a licence from the LEA to perform in most professional and some amateur contexts, and can only work a limited number of hours).
If your DD enjoys performing, I'd follow the advice above and look for some good-quality performing arts classes. If she's keen to be in a production, you could keep an eye out for audition calls put out by local theatre groups.
Amateur theatre can actually offer more chances to perform for a child who just loves being on stage. One of the most frustrating aspects of being on the professional audition circuit is that children rarely get to actually perform outside an audition room, because the industry is so competitive that the chances of being cast in any role are relatively small. And these days, most of them don't even get the chance to perform inside an audition room, because most first-round auditions are done via self-tape - film the audition at home, send it in to the agent or casting director...and never hear another word about it again. Feedback doesn't happen in this industry unless a child gets very close to being cast, and then it's usually just "the director thought someone else was a better fit for the role".
It takes quite a robust personality (child and parent!) to put a huge effort into tape and after tape without any tangible reward.
If you do decide to look for an agent in future, look for one which is a member of the AYPA (Agents of Young Performers Association). You should NEVER have to pay a fee to join an agency. You will usually be asked to pay a fee to join Spotlight, because that is the main online casting platform where agents submit clients for roles, but reputable agents earn money from commission on their client's earnings, so should only offer to represent a child that they think is talented enough to secure work. An agent will usually also ask you to get some professional headshots after you join an agency, but you don't need professional headshots to apply to an agency - any clear well-lit head-and-shoulders portrait on a phone camera is good enough for that. Prices for headshot photographers can be eye-watering, but there are plenty of good ones at the less painful end of the £££ scale.
If you are considering an agent, bear in mind that that the demands of auditions (and jobs) vary depending on the type of work. Agents like commercial work because it can pay well (so they earn a good chunk of commission). However, commercial auditions are more likely to be in-person and often operate to very short time-scales - as in, email at 4pm for an audition at 10am next morning, meaning a scramble to get permission from school and/or work for a morning off to dash into central London to spend 5 minutes (literally) inside an audition room. Commercials often "pencil" (provisionally book) several children for a job, so you do all the paperwork for a licence, arrange time off etc, the child gets excited, and then the pencil "snaps" and it's all off. However the time commitment if you actually get a commercial job is often relatively limited. Theatre and film auditions, on the other hand, often take place over a longer time-scale with more notice, but require a much bigger time commitment if cast (and kid's theatre pay is rubbish, even in the West End 😂).
The professional performing arts world is never dull, and my DS has had some fantastic experiences and worked with amazing actors, but it is a whole-family commitment and not for the faint-hearted!